You've hit the nail on the head - why is pedophilia wrong if homosexuality is right - particularly if 'informed consent' and be demonstrated in both? I always get "the difference is obvious" argument but no one explains why it's so obvious. From my perspective it's obvious why homosexuality is wrong but when I offer up my reasons they are discounted because they are a) religious in nature, b) suspect in their origins, c) refuted by other studies that demonstrate my studies just wrong because their study supports their point of view and mine's just obviously wrong.
This is no longer a hypothetical. There are actual psychologist and doctors that are stating that some forms of adult-child sex result not only in no harm for the child, but perhaps as a benefit. So if religion cannot be brought into the discussion how are we to combat this?
As far as why parents would do this, I don't know what is the issue in these cases but many people are afflicted with pedophile thoughts that they cannot control. Usually brought on through their upbringing. Now if their mind is feeling that sex with a child is truly a way of portraying love for that child, what do we tell them to prove to them that they are wrong? This is the same with homosexuals. They think that since they FEEL a certain way, it excuses them to act a certain way. And without using God, how do you oppose their views?
This is why a Godless law system can never work.